Summary The human brain is a large, well-connected, and dynamic network. Using functional MRI data, modeling how this network processes the stimulus information has yielded insight on some of the mechanisms of the brain. However, the past efforts, including ours, on using small-scale models yielded limited understanding of how the complete and dynamic neural system functions in task-related experiments. Such understanding cannot be recovered from the data without substantial and collaborative efforts on model development. Towards this goal, we formed a collaborative team from modelers to end-users, and we will develop large-scale methods for task related fMRI (tfMRI), including event-related fMRI, to model whole-brain network dynamics responding to task challenges. Using modern statistical learning principals and large-scale optimization algorithms, we will develop novel methods to model nonlinear, spatial-temporal dependence in high dimensional data of fMRI, stimuli, and behavior outcomes. We will primarily base our methods in the regularized, constrained graphical model (GM) framework, a promising multivariate framework for inferring brain connectivity that has been validated by simulation and anatomical studies. Using this framework, we will develop novel methods to investigate, at a large scale, how changes in connectivity and activation are driven by task challenges and how multiple brain pathways process stimulus information. We will perform comprehensive validation and assessment of the newly developed methods, using both simulated and multiple tfMRI data from large cohorts. Using the scale of modeling that previous approaches cannot readily address without substantial time penalties and maybe also inaccuracies, our collaborative team will also use these methods to investigate various novel questions and hypotheses concerning the neural basis for cognitive control as one of the use cases. We will also develop publicly available, open source implementations for a broad range of use in the neuroimaging community. These modeling efforts will lead to new insights on the networks of large-scale neural circuits, and provide pharmacological targets that may be overlooked using small-scale models.